Let object follow joined path
You can use these 2 ways to make the mesh follow path which isn't contiguous.

Making the path contiguous

This way assumes keyframing either the Evaluation time property of the curve:



or the Fixed Position option of the Follow Path constraint.



You set the keyframes so the animated mesh jumps from one curve part to another.



The mesh will now jump over the connection of the curves.



Adding several Follow Path Constraints

You can leave curves as they are, and add adjacent quantity of the Follow Path constraints, animating both Fixed Position and Influence options. 
For more details see How to make an object follow a complex curve